Reach the final battle with Darth Malak, but do not open the door yet. Press L + R on controllers one and four.

For these matrices:

Additive: 1, 2, 4, 7, 11, 16 (19, 22, 24, 31)
Subtractive: 21, 18, 16, 15, 15, 16 (14, 18, 19, 21)
Multiplicative: 1, 2, 4, 8, 16, 32 (48, 52, 64, 96)
Divisive: 128, 64, 32, 16, 8, 4 (2, 1, 0, -2)
Exponential: 1, 32, 81, 64, 25 (1, 3, 6, 9)
Logarithmic: 1 0 - 8 3 - 32 5 - 128 (5, 6, 7, 8)

The answers are: 22, 18, 64, 2, 3, 7. That will get you a security card to enter the Sith Private Hanger on Manaan.

Talk to the other members of your party often. Most have an extra side quest that can only be activated by talking to them at least 8 times during the game. Sometimes it takes even more. Bastila's, for example, has you searching for her mother on Tatooine and Carth's has you hunting for his lost son.

Finding Party Members
Bastila - Jedi Human - Taris
Canderous - Mandalorian Soldier - Taris
Carth - Human Soldier - Endar Spire
HK-47 - Combat Droid - Tatooine (buy him in the droid shop)
Jolee Bindo - Jedi Human - Kashyyyk
Juhani - Jedi Guardian - Dantooine (don't kill her!)
Mission - Tw'lek Scoundrel - Taris
Zaalbar - Wookie Scout - Taris
T3-M4 - Expert Droid - Taris

Anytime you are in a safe area (not in combat or inside a room) you can instantly heal yourself. Go to the Map screen in the pause menu and hit the X Button to instantly leap back to the Ebon Hawk. Your party members will be magically healed. You can then select the Map screen and hit X again to jump back to where you just were.